x^2-12x-5=-22 eching

$${ x }^{ 2 } -12x-5=-22$$

x uchun yechish

$$x=\sqrt{19}+6\approx 10,358898944$$

$$x=6-\sqrt{19}\approx 1,641101056$$

Kvadrat tenglamalaridan foydalanish qoidalari

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x^{2}-12x-5=-22$$

22 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}-12x-5-\left(-22\right)=-22-\left(-22\right)$$

O‘zidan -22 ayirilsa 0 qoladi.

$$x^{2}-12x-5-\left(-22\right)=0$$

-5 dan -22 ni ayirish.

$$x^{2}-12x+17=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -12 ni b va 17 ni c bilan almashtiring.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 17}}{2}$$

-12 kvadratini chiqarish.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 17}}{2}$$

-4 ni 17 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144-68}}{2}$$

144 ni -68 ga qo'shish.

$$x=\frac{-\left(-12\right)±\sqrt{76}}{2}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±2\sqrt{19}}{2}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±2\sqrt{19}}{2}$$

x=\frac{12±2\sqrt{19}}{2} tenglamasini yeching, bunda ± musbat. 12 ni 2\sqrt{19} ga qo'shish.

$$x=\frac{2\sqrt{19}+12}{2}$$

12+2\sqrt{19} ni 2 ga bo'lish.

$$x=\sqrt{19}+6$$

x=\frac{12±2\sqrt{19}}{2} tenglamasini yeching, bunda ± manfiy. 12 dan 2\sqrt{19} ni ayirish.

$$x=\frac{12-2\sqrt{19}}{2}$$

12-2\sqrt{19} ni 2 ga bo'lish.

$$x=6-\sqrt{19}$$

Tenglama yechildi.

$$x=\sqrt{19}+6 x=6-\sqrt{19}$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$x^{2}-12x-5=-22$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}-12x-5-\left(-5\right)=-22-\left(-5\right)$$

O‘zidan -5 ayirilsa 0 qoladi.

$$x^{2}-12x=-22-\left(-5\right)$$

-22 dan -5 ni ayirish.

$$x^{2}-12x=-17$$

-12 ni bo‘lish, x shartining koeffitsienti, 2 ga -6 olish uchun. Keyin, -6 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-12x+\left(-6\right)^{2}=-17+\left(-6\right)^{2}$$

-6 kvadratini chiqarish.

$$x^{2}-12x+36=-17+36$$

-17 ni 36 ga qo'shish.

$$x^{2}-12x+36=19$$

x^{2}-12x+36 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-6\right)^{2}=19$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{19}$$

Qisqartirish.

$$x-6=\sqrt{19} x-6=-\sqrt{19}$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{19}+6 x=6-\sqrt{19}$$